Information • T extbooks • Media • Resources
Logic vs Misconceptions in Undergraduate Organic Textbooks: Radical Stabilities and Bond Dissociation Energies Andreas A. Zavitsas Department of Chemistry, Long Island University, Brooklyn, NY 11201;
[email protected] Nine of ten textbooks for undergraduate organic chemistry that we happened to examine share a serious error in logic, to various extents. They all state, correctly, that the relative stability of alkyl radicals is tertiary > secondary > primary > methyl. One provides no explanation. The other nine provide a rationalization in terms of C–H homolytic bond dissociation energies: BDE[H3C–H] = 105.0 > BDE[CH3CH2–H] = 100.5 > BDE[(CH3)2CH–H] = 99.1 > BDE[(CH3)3C–H] = 95.2 kcal/mol. These values are derived from heats of formation, ∆Hf° at 298 K, given in the NIST database, the primary source of thermochemical data for this article (1). Textbooks generally provide a table of BDE values for common covalent bonds. The relative stability of the alkyl radicals formed by bond dissociation is equated, or related, to differences in BDE[R–H]. The general argument is that, since Hⴢ is a common product, the difference in energy required to break each bond must reflect the relative stability of each alkyl radical formed. The more stable Rⴢ is, the weaker the bond it makes and the easier it is to form. Accordingly, CH3CH2ⴢ is more stable than CH3ⴢ by 4.5 kcal/mol, (CH3)2CHⴢ by 5.9, and (CH3)3Cⴢ by 9.8. The argument that differences in BDE[R–H] reflect the relative stabilities of Rⴢ seems reasonable, but it is not. The logical error becomes obvious when one applies the same argument to the alcohol series. Differences in BDE[R–OH] should also reflect the relative stabilities of Rⴢ, since ⴢOH is a common product. However, the ordering of BDE values is now quite different: (CH3)2CH–OH = 96.5 > (CH3)3C–OH = 95.0 > CH3CH2–OH = 94.0 > H3C–OH = 92.4. Methanol has the weakest C–OH bond, and therefore it follows that methyl is the most stable alkyl radical, being the easiest to form. Similar results are obtained by applying the argument to R–Cl, R–NH2, R–OCH3, and R–F. BDE[CH3–X] is the weakest bond in these series also, and therefore methyl again must be the most stable alkyl radical! The problem here stems from failure to emphasize or inform students that BDE[A–B] is the energy difference between the final state and the starting state. The final state is certainly affected by the inherent stability of the product radicals Aⴢ and Bⴢ. The stability of the starting state, the undissociated A–B bond, is also affected by the polarity of the A–B bond, among other factors. This dipole effect can be estimated, to a good approximation, by straightforward application of Pauling’s well-known equation (eq 1).
radical stabilities that are independent of the nature of the precursor molecule. This can be accomplished by examining BDE[R–R] and the approach will be reliable in the absence of any complicating factors, such as strain energy weakening the R–R bond because of steric repulsion between two bulky R groups, as is the case with R = (CH3)3C. To obtain the stability of Rⴢ relative to that of CH3ⴢ, one must compare BDE[R–R] to BDE[H3C–CH3]; this will eliminate any ∆χ effect. Alternatively, the ∆χ effect can be minimized by approximating the relative stabilities of various Rⴢ vs CH3ⴢ by comparing BDE[R–CH3] to BDE[H3C–CH3]. We adopt the latter approach here because (i) steric strain effects are minimized and (ii) many textbooks already include BDE[R-CH3] in their tables. Stabilization energies (SE) of carbon radicals relative to methyl are estimated by eq 2, using the BDE values given in Table 1. SE[Rⴢ] = BDE[H3C–CH3] – BDE[R–CH3]
(2)
The results are described below and then eq 1 is used to calculate BDE[R–X] for simple compounds, for which BDE values are usually tabulated in undergraduate texts. This approach resolves the conundrum demonstrated in the second paragraph, provides an insight into starting state and final state effects, and is sufficiently straightforward for undergraduates. From the BDE[R–CH3] values given in Table 1 and eq 2, SE[CH3ⴢ] = 0.00, SE[CH3CH2ⴢ] = 1.74, SE[(CH3)2CHⴢ] = 1.07, SE[(CH3)3Cⴢ] = 4.00, SE[CH2=CHCH2ⴢ] = 14.04, and SE[C6H5CH2ⴢ] = 12.74 kcal mol᎑1. These SE values are considerably smaller than those obtained from BDE[R–H] values. Equation 2 provides a good approximation to relative stabilization energies. The resulting SE values adequately reproduce literature values for BDE of any combination of alkyl groups. Table 1. Calculated and Literature Values of BDE BDE/kcal mol᎑1 a Rⴢ
Me 0.00
Et 1.74
i - Pr 1.07
t - Bu 4.00
Allyl 14.04
PhCH2 12.74
Ref
Me
90.24 89.9
88.5 88.9
89.2 88.7
86.24 87.2
76.2 76.1b
77.5 79.4
1 3
87.17 86.8
87.1 87.4
83.8 84.5
74.4 74.5
76.0 75.8
1
86.49 88.1
82.0 85.2
74.7 75.1
76.7 76.4
1
76.0 82.2
71.9 72.2
73.5 73.5
1
61.40 62.2
63.4b 63.5
1
66.60
1
Et i - Pr
BDE[A–B] = 1⁄2(BDE[A–A] + BDE[B–B]) + 23(∆χ)2 (1)
t - Bu
∆χ is the electronegativity difference between atoms, or groups, A and B (2). In essence, ∆χ is defined by eq 1. The ∆χ term has no effect on the stability of the final state, where Aⴢ and Bⴢ are separated; it affects the starting state only. If we try to estimate relative stabilities of the carbon radicals by using BDE data, as many textbooks do, we must eliminate or minimize any effect of ∆χ. Then we can obtain relative
Allyl PhCH2
64.8
a Values in boldface were used as data to calculate relative stabilization energies (SE). Literature values are in regular type. Values calculated by eq 3 are in italic. b ∆H ° of compound from ref 4 and ∆H ° of radicals from ref 1. f f
JChemEd.chem.wisc.edu • Vol. 78 No. 3 March 2001 • Journal of Chemical Education
417
Information • Textbooks • Media • Resources
This is demonstrated in Table 1, where literature values are compared to BDE[R–R′] calculated using the corresponding SE values. From the rationale of eq 2, it follows that BDE[R–R′] is given by eq 3, which produces BDE values for a hypothetical, strain-free molecule. BDE[R–R′] = BDE[H3C–CH3] – SE[Rⴢ] – SE[R′ⴢ] (3) Therefore, calculated values for molecules that are expected to be subject to steric strain should be higher than those measured experimentally. This is the case for the following three bonds. For BDE[(CH3)3C–C(CH3)3], the calculated strain-free value is 6.2 kcal mol᎑1 greater than experimental. This strain energy has been calculated by Rüchardt et al. (5) as 6.9 kcal mol᎑1, in good agreement. The calculated BDE[(CH3)2CH–CH(CH3)2] is also higher than the experimental value by 1.6 kcal mol᎑1, while Rüchardt et al. calculate 2.7 kcal mol᎑1 of strain energy. For the cross combination, the calculated BDE[(CH3)3C– CH(CH3)2] is 3.2 kcal mol᎑1 greater than experimental, a value between those of the two symmetrical hydrocarbons. Excluding these three molecules, the other 12 entries in Table 1 show an average deviation of 0.4 kcal mol᎑1 between literature values and those calculated from SE[Rⴢ] and eq 3. By comparison, BDE[H3C–R] values from common databases (1, 3, 4 ) in Table 1 show an average deviation of 0.7 kcal mol᎑1 among themselves. Can SE[Rⴢ] values calculated by eq 2 be used to estimate BDE[R–X] values that are consistent with experiment? This is accomplished by using eq 1, where BDE[A–A] represents BDE[R–R], the calculated strain-free BDE for the symmetrical hydrocarbons from Table 1, and BDE[B–B] represents BDE[X–X] from the literature for X = OH, Cl, NH2, OCH3, and F, given in Table 2. An electronegativity scale can now be established by arbitrarily assigning χ[OH] = 3.500, adopting
Pauling’s value for oxygen (2). The assigned value per se is inconsequential, since eq 1 uses only differences in electronegativity, ∆χ. We chose χ[OH] as the anchor point because values of BDE[R–OH] are known accurately and are routinely included in BDE tables. Equation 1 is now used to calculate χ values for all Rⴢ in Table 1 from the calculated strain-free BDE[R-R] and the literature values of BDE[R-OH] and BDE[HO-OH]. Solving for ∆χ leads to χ[CH3ⴢ] = 2.528, χ[CH3CH2ⴢ] = 2.458, χ [(CH 3) 2 CHⴢ] = 2.419, χ [(CH 3 ) 3Cⴢ]= 2.390, χ[CH2=CHCH2ⴢ] = 2.498, and χ[C6H5CH2ⴢ] = 2.498. Similarly, χ[Xⴢ] values for X = Cl, NH2, OCH3, and F are calculated by solving eq 1 for ∆χ for each X, with the above value of χ [CH3ⴢ] and literature values of BDE[CH3–X] and BDE[X–X]. The resulting χ values are given in Table 2. BDE values for any combination of R–X can now be calculated. Twenty values of BDE[R–X] calculated in this way are shown in Table 2 and they agree with literature values generally to within ±1 kcal mol᎑1. The effect of relative stabilization energies (SE) and electronegativity differences (∆χ ) on BDE is illustrated by focusing on one example. Compared to BDE[CH3–OCH3], BDE[CH3CH2–OCH3] should be weaker by 1.74 kcal mol᎑1, the stabilization energy of the ethyl radical relative to methyl in the final state, the radical products. The starting state, the undissociated R–OCH3 bond, should be strengthened in CH3CH2–OCH3 by an electronegativity effect of 23(∆χ)2 = 23(3.437 – 2.458)2 = 22.04 kcal mol᎑1 and in CH3–OCH3 by 23(3.437 – 2.528)2 = 19.00; the ∆χ effect should make the CH3CH2–OCH3 bond stronger by 22.04 – 19.00 = 3.04 kcal mol᎑1. The net result is a calculated BDE stronger in CH3CH2–OCH3 by 3.04 – 1.74 = 1.3 kcal mol᎑1 vs CH3–OCH3. Table 2 shows literature values of 1.0 kcal mol᎑1 stronger (1) and 1.6 stronger (3), in excellent agreement.
Table 2. Values of BDE [R–X] and Calculated Electronegativities BDE[R–X] / kcal mol ᎑1 a X = OH χ = 3.500
R
Value
Ref
X = Cl χ = 3.188 Value
Ref
X = NH2 χ = 3.076 Value
Ref
X = OC H3 χ = 3.437 Value
Ref
X=F χ = 3.942 Value
Ref
Me χ = 2.528
92.42 92.5
1 3
84.12 83.4
1 3
86.13 84.6
1 3
83.22 83.2
1 3
110.08 112.8
1 3
Et χ = 2.458
93.95 94.4
1 3
84.2 84.4 84.6
1 3
84.6 87.0 86.3
3 6
84.2 84.8 84.5
1 3
110.7 113.7 113.1 113.0
3 7 8
i - Pr χ = 2.419
96.51 96.1
1 3
85.7 85.1 86.6
1 3
87.5 85.8 88.1
1 3
86.3 86.0 87.0
1 3
110.7 117.2 116.4 116.4
1 7 8
t - Bu χ = 2.390
95.02 96.3
1 3
83.0 84.9 84.8
1 3
85.3 85.6 86.0
1 3
82.8 84.4 85.4
1 3
119.9 116.4 115.5
7 8
Allyl χ = 2.498
79.77 80.2b
1
71.2 71.0
1
75.4b 73.1 72.9
81.09 PhCH2 χ = 2.498 81.3
1 3
74.0 72.4 72.4
1 3
X–X c
1
57.98
1
51.17
4
70.0b 67.7 70.5
4
96.9b 97.4 98.0
74.0 71.1 74.2
1 3
71.6b 71.8
3
98.7 98.6 99.4
68.21
1
38.2
1
37.94
9 1,8 9 1
aValues
in boldface were used as data. Literature values are in regular type. Values calculated by eq 1 are in italic. b∆H ° of compound from ref 4 and ∆H ° of radicals from ref 1. f f cBDE of the symmetrical compounds HO–OH, Cl–Cl, H N–NH , CH O–OCH , and F–F. 2 2 3 3
418
Journal of Chemical Education • Vol. 78 No. 3 March 2001 • JChemEd.chem.wisc.edu
Information • Textbooks • Media • Resources
Two things are worth noting: (i) the ∆χ effect is greater than the SE effect, and (ii) in BDE[CH3–OCH3] = 84.5, a substantial 19.0 kcal mol᎑1 is due to the effect of ∆χ on the starting state, the undissociated bond. Discussion of shortcomings associated with eq 1 is beyond the scope of this article. The nature of the chemical bond is too complex to be fully described by this simple relationship. Nevertheless, along with properly defined SE values, eq 1 does account for the major factors affecting BDE for the molecules examined in this work. Literature Cited 1. Afeefy, H. Y.; Liebman, J. F.; Stein, S. E. Neutral Thermochemical Data; in NIST Chemistry WebBook; NIST Standard Reference Database Number 69; Mallard, W. G.; Linstrom, P. J., Eds.; National Institute of Standards and Technology: Gaithersburg MD, Nov 1998; http://webbook.nist.gov (accessed Oct 2000). BDE[A–B] = ∆Hf°[Aⴢ] + ∆Hf°[Bⴢ] – ∆Hf°[AB]. When values are not available in this database, other sources are used as specified.
2. Pauling, L. The Nature of the Chemical Bond and the Structure of Molecules and Crystals, 3rd ed.; Cornell University Press: Ithaca, NY, 1960. 3. Handbook of Chemistry and Physics, 77th ed.; Lide, D. R., Ed.; CRC Press: Boca Raton, FL, 1996–1997. 4. Stein, S. E. Structures and Properties, Version 2.0 in NIST Standard Reference Database No. 25, January 1994; National Institute of Standards and Technology: Gaithersburg, MD. Data evaluated by S. G. Lias, J. F. Liebman, R. D. Levin, and S. A. Kafafi. 5. Rüchardt, C.; Beckhaus, H.-D. Angew. Chem. 1985, 24, 529–538. 6. Curtiss, L. A.; Raghavachari, K.; Redfern, P. C.; Pople, J. A. J. Chem. Phys. 1997, 106, 1063–1079. G2 calculation. 7. Luo, Y.-R.; Benson, S. W. J. Phys. Chem. 1997, 101, 3042– 3044. 8. Schaffer, F.; Verekin, S. P.; Rieger, H. J.; Beckhaus, H. D.; Rüchardt, C. Liebigs Ann. Chem. 1997, 1333–1344. From the experimental heats of formation of nonyl fluoride for CH3CH2–F and of cyclohexyl fluoride for (CH3)2CH–F and the resulting group additivity values. Group additivity for (CH3)3C–F. 9. Zavitsas, A. A. J. Phys. Chem. 1987, 91, 5573–5577.
JChemEd.chem.wisc.edu • Vol. 78 No. 3 March 2001 • Journal of Chemical Education
419
